preface - don bosco school
TRANSCRIPT
PREFACE
I take great pleasure in presenting this Mathematics Assignment Booklet for
Class 6 for the academic session 2019-2020. This booklet has been written in
accordance with the CBSE and NCERT pattern. Through this Booklet, I want to
supplement the teaching material in the textbook. This booklet is aimed at
providing ample practice to the students in the various mathematical concepts so
that they may grasp these concepts and effectively apply them, with sufficient
drill and practice. I also hope this booklet will stimulate the students‟ mind and
interest in Mathematics.
One of the unique features of this booklet is the variety of exercises that have
been incorporated. The questions have been presented in a lucid manner so as
to arouse the interest of the students in mathematics and to develop problem-
solving skills in them along with logical and lateral thinking. These worksheets
will help the students to quickly test their knowledge and skills. The booklet
especially aims to make Mathematics enjoyable through activities, crosswords,
and enrichment exercises that appeal to students. Keeping in mind that the level
of understanding of each student may differ at any point of time, an effort has
been made to introduce questions progressively such that each student gains
confidence and learns concepts in an organized manner. The Sample test
papers at the end of the booklet will help better equip students for their exams as
they self-administer these tests to simulate examination conditions.
I would also like to take the opportunity to express my sincere appreciation to
Father Babu Varghese, our school Principal, for his constant support, guidance
and encouragement. I am also grateful to Mr. Baiju Mathew, our subject
coordinator for Mathematics, for believing in me and for his support and
suggestions in preparing this booklet.
I welcome any suggestions for improvement and I shall acknowledge and
incorporate them in the subsequent edition.
Thank you!
Mrs. Jyoti Kohli, TGT (Mathematics)
Don Bosco School, Alaknanda, New Delhi
i
CONTENTS
S.No. Topic Page Number
1) Syllabus 1
2) Assignment 1A – Knowing Our Numbers………………. 6
3) Assignment 1B – Knowing Our Numbers………………. 9
4) Assignment 2 – Whole Numbers………………………. 12
5) Assignment 3A – Playing With Numbers……………… 16
6) Assignment 3B – Playing With Numbers……………… 22
7) Assignment 4 – Basic Geometrical Ideas…………….. 28
8) Assignment 5 – Understanding Elementary Shapes… 39
9) Assignment 6 – Integers………………………………… 46
10) Assignment 7 – Fractions……………………………….. 48
11) Assignment 8 – Decimals………………………………. 52
12) Assignment 9 – Data Handling…………………………. 54
13) Assignment 10 – Mensuration…………………………… 57
14) Assignment 11 – Algebra………………………………… 59
15) Assignment 12 – Ratio and Proportion…………………. 61
16) Assignment 13 – Symmetry……………………………… 64
17) Assignment 14 – Practical Geometry…………………… 67
18) Sample Paper 1 – PT1……………………………………... 69
19) Sample Paper 2 – PT2……………………………………… 71
20) Sample Paper 3 – PT3……………………………………… 74
21) Sample Paper 4 – Annual Examination………………….. 77
- 1 -
Syllabus Academic Session 2019-20
Periodic Test 1
Chaper 1 – Knowing Our Numbers
Indian System of Numeration
International System of Numeration
Number Names
Write as numeral
Place Value, Face Value and Period
Expanded Form
Short Form
Comparing Numbers
Ordering of Numbers
How many numbers can you make?
Forming numbers with conditions
Shifting digits
Large Numbers in Practice
Simplification Using BODMAS rule (Not in textbook)
Rounding Numbers
Estimation of outcomes of number situations with respect to sum, difference and product
Using Brackets
Expanding Brackets
Roman Numerals till 3999
Chaper 2 – Whole Numbers
Introduction to the concept of whole numbers
Predecessor and successor
Number Line
Addition, Subtraction and multiplication on Number Line
Properties of Whole Numbers - Closure, commutative, associative properties with
respect to four basic operations, Identity (for addition and multiplication), Distributive
property
Patterns in Whole Numbers – Shapes made of dots as line, rectangle, square and
triangle
Chapter 13 – Symmetry
Figures with one, two or multiple lines of Symmetry
Symmetry in Alphabets
Symmetry in Geometrical Shapes – Rectangle, Square, Rhombus, Parallelogram, Circle,
Scalene Triangle, Isosceles Triangle, Equilateral Triangle.
Reflection and Symmetry
- 2 -
PROJECT – 1) Symmetry in Objects, nature, animals
2) Making Symmetric Figures – Ink Blot Devils, Inked-String Patterns, Paper
Folding and Cutting (Any Two)
3) Symmetry in Alphabets – Write your name with cutouts of Alphabets and
draw all possible lines of Symmetry with sketch pen
4) Symmetry in Geometrical Shapes – Rectangle, Square, Parallelogram,
Rhombus, Circle.
Syllabus for Half Yearly Examination
Periodic Test 2
Chapter 1 - Knowing Our Numbers and Simplification using BODMAS Rule (Assignment
1A and 1B)
Chapter 2 – Whole Numbers (Assignment 2)
Chapter 3 – Playing With Numbers
Factors and Multiples
Prime and Composite Numbers
Tests of Divisibility of Numbers 2, 3, 4, 5, 6, 8, 9, 10, 11
Common Factors and Common Multiples
Some More Divisibility Rules
Prime Factorisation
Highest Common Factor (HCF) and Lowest Common Multiple (LCM)
Some Problems on HCF and LCM
Chapter 4 – Basic Geometrical Ideas
Points
Line Segment
Line
Intersecting Lines
Parallel Lines
Ray
Curves
Polygons
Angles
Triangles
Quadrilaterals
Circles
- 3 -
Chapter 6 – Integers
Number Line
Predecessor and Successor
Tag Numbers with a Sign
Representation of integers on a number line
Ordering of integers
Addition and Subtraction of Integers
Addition and Subtraction of integers on a number line
Subtraction of Integers with the help of a Number Line
Chapter 7 – Fractions
Write the fraction represented in given
Fraction on the Number Line
Proper, Improper and Mixed Fractions
Express mixed fractions as improper fractions and vice versa
Equivalent Fractions
Simplest Form of a Fraction
Like Fractions
Comparing Fractions
Addition and Subtraction of Fractions
Chapter 13 – Symmetry (Assignment 13)
Syllabus for Periodic Test 3
Chaper 8 – Decimals
Decimal Place Value Chart
Pictorial Representation of Decimal numbers
Naming Decimal numbers in words
Representing Decimals on number line
Short Form and Expanded Forms of Decimals
Fractions as decimals
Decimals as fractions
Comparing decimals
Using Decimals in Money, Length and Weight
Addition of Numbers with Decimals
Subtraction of Decimals
- 4 -
Chaper 9 – Data Handling
Recording data
Organization of Data using tally marks
Pictograph
Interpretation of a Pictograph
Drawing a Pictograph
Bar Graph
Interpretation of Bar Graph
Drawing a Bar Graph
Chapter 10 – Mensuration
Perimeter
Perimeter of Rectangle and regular shapes
Area by counting squares
Area of rectangle and square
Chapter 11 – Algebra
Matchstick Patterns in Algebra to establish general rule
Use of Variables in Common Rules
Expressions with Variables
Using Expressions Practically
Equation and its solution
Syllabus for Annual Examination
Chapter 5 – Understanding Elementary Shapes (Assignment 5)
Measuring Line Segments
Angles – „Right‟ and „Straight‟
Angles – „Acute‟, „Obtuse‟ and „Reflex‟
Measuring Angles
Perpendicular Lines
Classification of Triangles
Quadrilaterals
Polygons
Three Dimensional Shapes
Chapter 6 – Integers (Assignment 6)
- 5 -
Chapter 8 – Decimals (Assignment 8)
Chapter 9 – Data Handling (Assignment 9)
Chapter 10 – Mensuration (Assignment 10)
Chapter 11 – Algebra (Assignment 11)
Chapter 12 – Ratio and Proportion (Assignment 12)
Ratio
Proportion
Unitary Method
Chapter 14 – Practical Geometry (Assignment 14)
Constructions with RULER and COMPASSES
Construction of circle with known radius
Construction of a line segment of a given length (using ruler and compasses)
Constructing a copy of a given line segment
Perpendicular to a line through a point on it.
Perpendicular to a line through a point not on it.
The perpendicular bisector of a line segment
Constructing an angle of a given measure
Constructing a copy of an angle of unknown measure
Bisector of an Angle
Angles of special measures : 30°, 45°, 60°, 90°, 120°, 135°.
- 6 -
Knowing Our Numbers
Assignment 1(A)
1. Write in figures:
(i) Forty-five millions, nine thousand, thirty four
(ii) Nine lakhs, four thousand, three hundred five
(iii) Twenty one lakhs, twelve thousand, two hundred
(iv) Six millions, two hundred one thousand, five hundred three
(v) Fifty-six millions, eight hundred sixty-four
2. Look at the placement of commas and write in Words, using appropriate system of
Numeration:
(i) 7,413,001 (ii) 4,57,398 (iii) 6,005,173
(iv) 8,061,481 (v) 91,00,845
3. Fill in the blanks:
(i) _______ thousand = 1 million
(ii) _______ lakhs = 10 millions
(iii) _______ millions = 1 crore
(iv) 10 lakhs = _______ million
(v) 100 thousand = _______ lakh
4. Write the numerals (with commas) for each of the following:
(i) 60 00 000 + 3 00 000 + 90 000 + 6000 + 40 + 7
(ii) 80 00 00 000 + 6 00 00 000 + 8 00 000 + 60 000 + 7 000 + 200 + 60 + 5
(iii) 2 0 000 000 + 8 000 000 + 500 000 + 10 000 + 7 000 + 300 + 70 + 4
(iv) 500000 + 20000 + 4000 + 300 + 70 + 8
(v) 7 00 00 000 + 9 00 000 + 70 000 + 800 + 50 + 6
5. Write in expanded form :
(i) 14,53,826 (ii) 25,327,428 (iii) 1,05,75,945
(iv) 8,29,100 (v) 3,030,305
6. Compare the following numerals by inserting >, < or = in the space provided:
(i) 14,53,826 ______ 15,43,826
(ii) 71,21,493 ______ 7,21,493
(iii) 8,29,100 ______ 8,92,100
(iv) 17,82,135 ______ 1,782,135
(v) 852,327,428 ______ 853,327,428
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MISCELLANEOUS QUESTIONS
1. Fill in the blanks :
(i) The thousands period has ____________ places in Indian System of numeration.
(ii) In _______________ system of numeration 100000 is read as „one hundred
thousand‟?
(iii) ______________ place is just to the left of thousands place?
(iv) ______________ place is just to the right of lakhs place?
(v) The greatest five digit even number is ________________
(vi) In the International system the next period to the left of thousands is ___________
(vii) The greatest 6-digit number using the digits 0, 1 and 2 (each digit used at least once) is
_______
(viii) One thousand less than one lakh is _______________
(ix) 97658 + ___________ = 100000
(x) 7312097 - _____________ = 2594873.
(xi) 12743 x 200 = 127430 x ____________
2. Look at the pattern and write the next three numbers: 2134509, 2334509, 2534509.
3. Write the place value of 7 in 87,23,014.
4. Write place value of 2 in 18,270,014.
5. Write in ascending order : 7617617, 7617671, 7617167, 7611761.
6. Write the smallest number using all the digit once : 1, 3, 0, 6, 7, 8.
7. Write the greatest number using all the digits once : 2, 1, 4, 3, 5, 8.
8. Write the smallest 6-digit number.
9. Write the greatest 7 digit number.
10. Write the greatest possible 5-digit number using the digits : 1, 0, 5, 6
11. Write the smallest possible 6-digit number using the digits : 6, 0, 3, 5
12. Solve:
(i) 17102 x 15
(ii) 5279 x 3000
(iii) 32897 ÷ 100
(iv) 105182 ÷ 683
(v) 652497 - 583217
13. The cost of 40 radio sets is Rs. 24880. Find the cost of one radio set.
14. 540870 metres of rope is to be packed in bundles of 100 metres each. How many
bundles will be made and how much rope will remain unpacked?
15. A cargo plane can carry 153742 kg per trip. How many kg can it carry in 28 trips?
16. How much is 13692 less than 300000?
17. The population of Lalnagar in the year 2008 was 3,24,517. In year 2018 it was found to
be increased by 27,598. What was the population of the city in 2018.
18. Complete the blanks in the given cheques :
- 8 -
Dated : …………...…
Pay ……Mrs Chandrashekhar.........................................................
Rupees…Seven lakhs, five hundred only….……………………………………..
……………………………………………..…………………………………………………...
Signature
Dated : …………...…
Pay …… M/s International Aircon Ltd................................................
Rupees……………………………………………………………………………………….
……………………………………………..…………………………………………………...
Signature
Rs……………………...
Rs…6,41,009..…...
- 9 -
Knowing Our Numbers
Assignment 1(B)
1. Simplify using BODMAS Rule:
(i) 24 ÷ 6 + 5
(ii) 10 ÷ 5 + 8 ÷ 2
(iii) (5 – 2) x 7 + 9
(iv) 8 – 4 ÷ 2 x 3 + 5
(v) 45 ÷ 15 x 2 + 18 - 7
(vi) 112 x 6 ÷ 3 -16 + 1
(vii) 15 – 5 x 2 + 3
(viii) 132 - 45 ÷ 15 x 12 + 10
(ix) 31 - 4 + 3 ÷ 3 x 2
(x) 47 + 6 ÷ 3 x 2 – 38
(xi) 4 x 12 + 3 x 3 ÷ 3 + 15 - 4
(xii) 82 ÷ 2 x 6 - 48 + 3 x 5
(xiii) 72 ÷ 12 x 2 + 6 - 3
(xiv) 24 - 10 ÷ 5 + 2 x 3
(xv) 30 + 6 ÷ 3 - 2 x 5
(xvi) 40 ÷ 5 x 2
(xvii) 16 + 4 x 6 ÷ 2 - 7
(xviii) 30 - 9 x 8 ÷ 4
2. Re-write each of the following expressions putting in brackets so that each one is equal
to 30. Example: 2 x 3 + 24 would be (2 x 3) + 24 = 30.
(i) 11 x 3 – 3
(ii) 10 + 5 x 4
(iii) 3 + 2 x 6
(iv) 3 x 5 + 3 x 5
(v) 30 ÷ 5 + 24
(vi) 2 x 10 + 2 x 5
(vii) 12 + 3 x 2 + 3 x 4
(viii) 12 x 2 + 2 + 2 x 2
(ix) 2 + 5 x 2 + 4 x 4
(x) 47 + 6 ÷ 3 x 2 – 38
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3. Write the expressions for each of the following using brackets.
(i) Four multiplied by the sum of nine and two.
(ii) Divide the difference of eighteen and six by four.
(iii) Multiply the difference of 7 and 3 by the sum of 11 and 9.
4. Solve using expanding brackets :
(i) 7 × 109
(ii) 102 × 103
(iii) 17 × 109
(iv) 206 x 9
5. Round these numbers to the nearest tens:
28 32 99 215 1453 2936
6. Round these numbers to the nearest hundreds:
168 4546 6850 8760 53552
7. Round these numbers to the nearest thousands:
841 5750 9870 9537 49730
8. Estimate to nearest thousands: 5,290 + 17,986
9. Find the difference of 456 and 699 by rounding the numbers to the nearest tens.
10. Estimate by General Rule: (i) 5,673 – 436 (ii) 838 + 234 + 4,318
11. Estimate the following products to nearest hundreds:
(i) 87 × 313 (ii) 9 × 795
12. Estimate the following products by General rule:
(i) 898 × 785 (ii) 958 × 387
13. Complete the following :
(i) DCL = 500 + _____ + _____ = _____
(ii) CCXXI = _____ + 20 + _____ = _____
(iii) XIV = 10 + _____ = _____
(iv) MCXL = _____ + _____ + _____ = _____
14. Which of the following numerals are meaningless ?
(i) IXIV (ii) CCCI (iii) ICC (iv) MC (v) DM
(vi) MXXVII (vii) LCXVI (viii) CIC (ix) CMXIV (x) IXX
- 11 -
15. Write the standard form for the year :
(i) Sound movies were invented in MCMXXVII.
(ii) Air conditioning was invented in MCMXL.
(iii) The toaster was invented in MCMXVIII.
(iv) The lawn mower was invented in MDCCCLXVIII.
16. Choose the correct numeral from the following numerals given in pairs:
(i) IIII, IV (ii) MMMM, IV (iii) XIV, IXV
(iv) XXXIX, IXXXX (v) IXX, XIX (vi) IXXV, XXIV
17. Rewrite the following Hindu-Arabic numerals as roman numerals:
(i) 14 (ii) 67 (iii) 452 (iv) 994 (v) 678
(vi) 90 (vii) 556 (viii) 1987 (ix) 2876 (x) 3765
18. Rewrite the following Roman Numerals as Hindu Arabic numerals :
(i) CLXVI (ii) CMXLIV (iii) LXXXVIII (iv) LXXIX (v) LI
(vi) XXXIV (vii) LXIV (viii) XLIX (ix) MDXIX (x) MMMCMXCIX
19. Write <, > or = in the blank to make the following true:
(i) XXIX _______ XXXI (ii) XC ________ XL (iii) L _______ LX
(iv) XLIX ________ LXIX (v) 97 _______ XCVII (vi) XC _______ CX
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Whole Numbers
Assignment 2
1) Fill in the blanks with the correct answer:
(i) 82 ÷ 1 is ______________
(ii) The product of two odd numbers is ___________
(iii) The property represented by a × (b + c) = (a × b) + (a × c) is ___________________
(iv) 6×(7 × 3) = (6 × 7) ×3 is an example of _______________ property
(v) Successor of 301,999 is ____________
(vi) 38 + 83 = 83 + 38 is an example of _________________ property
(vii) Closure property is satisfied in whole numbers with respect to ________ and _________
(viii) Adding two whole numbers always gives a _________________
(ix) 42× (4 + 2) = (42 × 4) + (42 × 2) is an example of __________________ Property
(x) (98 + 14) × 0 is ________________
(xi) The whole numbers between 0 to 5 are____________________
(xii) The additive identity element of 24 is ____________
(xiii) The three consecutive predecessors of 70010 are ________, _______, _______
(xiv) The difference between the face values of 5 and 9 in 165,234, and 842,928 is __
(xv) The least natural number is ____________
(xvi) Division by zero is _____________
2) Fill in the blanks with the correct answers:
(i) (4 x 56) + (4 x 4) = (12 x 100) – (______ x 5)
(ii) 184 x 96 + 184 x 4 = ______________
(iii) 847 x 193 – 193 x 747 = _______________
(iv) 12 x 40 + 12 x 8 = 12 x ____________
(v) 736 x 102 = 736 x ( 100 + ______ )
(vi) 654 x 99 = 654 x ( 100 - _____ )
(vii) 124 x 273 = ( _____ + ______ + _____ ) x 273
(viii) 35 x 197 – 35 x 90 – 35 x 7 = ______________
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3) Which of the following properties is not applicable to the subtraction of Whole numbers?
(A) Closure Property
(B) Commutative Property
(C) Associative Property
(D) All the three
4) Commutative Property holds good only in which operations?
(A) Addition and subtraction
(B) Addition and multiplication
(C) Addition and division
(D) None of them
5) State True or false and correct the wrong statement
(i) Sum of two odd numbers is always odd.
(ii) Every whole number has its predecessor.
(iii) Is b ÷ a = a ÷ b where a, b are natural numbers.
(iv) The smallest 4– digit numbers ending with 5 is 1005.
6) Properties of whole numbers : write true or false in the appropriate cells
Property Addition Subtraction Multiplication Division
Closure Property
Commutative Property
Associative Property
Identity Element
7) What is the number by which when we multiply any number, the product remains same as
the number?
8) Which natural number has no predecessor?
9) What is the difference between the largest 5-digits number and smallest 5-digits number?
10) What are the numbers which we use for counting.
11) How many whole numbers are between 22 and 50?
12) Write the successor and predecessor of 500390?
13) What is the product of a whole number and zero?
- 14 -
14) What is the multiplicative identity element of whole numbers?
15) Find the sum by suitable rearrangement:
a. 165 + 578 + 335 b. 373 + 227 + 667 c. 268 + 415 + 332 d. 557 + 288 + 143 + 12
16) Find the product using the properties of multiplication:
a. 625 x 3 x 16 b. 25 x 89 x 40 c. 4 x 1365 x 25 d. 4 x 2 x 25 x 5
17) Use distributive property to solve:
(i) 12 x 35
(ii) 7 x 109
(iii) 102 x 103
(iv) 567 x 103
(v) 25 x 166 + 25 x 134
(vi) 87 x 1010
(vii) 47 x 103 – 47 x 3
(viii) 105 x 97
18) Solve using suitable Property:
(i) The school canteen charges Rs 20 for lunch and Rs 4 for milk for each day. How much
money do you spend in 5 days on these things?
(ii) Two members of a family work for 6 days a week in a factory. The husband is paid Rs.
15 each day and the wife Rs. 12 each day. Find their total earnings for a week. (Use
suitable property)
(iii) There are 15 boys and 15 girls in a class. They are collecting money for a cause. Each
boy collected Rs 253 and each girl collected Rs 247. How much money was collected by
the class?
(iv) Neha buys 456 books and 544 notebooks. If the cost of a book and a notebook is Rs 25
each, find how much total money does she spend?
(v) The product of two numbers is 504347. If one of the numbers is 317, find the other
number.
(vi) The digits 5 and 7 are interchanged in the number 27658 find the difference between the
original number and the new number.
(vii) The distance between Salma‟s house and Meera‟s house is 1km 750m. Every day
Salma walks both ways. Find the total distance covered by Salma in four days.
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19) Add using number line: (i) 3, 6 (ii) 0, 4
20) Subtract using number line: (i) 3 from 9 (ii) 4 from 7
21) Multiply using number line: (i) 2 x 4 (ii) 5 x 2
22) What mathematical operation to the following numbers represent:
(i) Ans : ____ ⎕ ____ = ____
(ii) Ans : ____ ⎕ ____ = ____
(iii) Ans : ____ ⎕ ____ = ____
23) Which numbers can be shown only as a line?
24) Which can be shown as squares?
25) Which can be shown as rectangles?
26) Write down the first seven numbers that can be arranged as triangles, e.g. 3, 6, ... 5.
27) Some numbers can be shown by two rectangles, for example,
Give at least five other such examples.
- 16 -
Playing With Numbers
Assignment 3A
1. Write true or false :
(a) 3 and 8 are factors of 48. __________
(b) 7 is a factor of 90 __________
(c) 5 is a factor of 135. __________
(d) 12 is a factor of 82. __________
(e) 128 is a multiple of 8 __________
(f) 152 is a multiple of 12 __________
(g) 205 is a multiple of 15. __________
2. Cross out the numbers which are not multiples of the given underlined numbers:
(a) 8 - 24, 40, 76, 80, 94
(b) 11 - 44, 61, 77, 99, 144
(c) 14 - 28, 56, 72, 98, 126
3. List the following numbers: (a) The next 5 even numbers after 78980 are __________, ___________,
___________, _____________, _____________
(b) The next 5 multiples of 5 after 87585 are __________, ___________,
___________, _____________, _____________
(c) All factors of 30 are _____________________________.
(d) All even numbers are multiples of ______________.
(e) Numbers with 0 or 5 in the ones place are multiples of _____________.
(f) Multiples of 10 have _________ in the ones place.
(g) 7 x 9 = 63, thus, 63 is a ______________ of 7 and 9
(h) 6 x 8 = 48, thus, 6 and 8 are ____________ of 48.
4. True or false:
a. 1 is a prime number. _________
b. 1 is a composite number _________
c. 2 is the only even prime number. _________
d. There is no greatest prime number. _________
- 17 -
5. The prime number 13 and 31 have the same digits. Write two more pairs of such prime
numbers. _______ , ________ and _________ , ________.
6. Pairs of prime numbers that differ by 2 are called twin primes. Example, 5 and 7 (7-5=2)
(i) Write the pairs of prime numbers between 1 and 100 that differ by 2
(ii) Write the pairs of prime numbers between 1 and 100 that differ by 3.
(iii) Write the pairs of prime numbers between 1 and 100 that differ by 6. They should also
be next to each other in the prime number sequence.
7. Write the prime numbers which come just before :
(a) 20 ________ (b) 40 ________
(c) 60 ________ (d) 80 ________
8. Write the composite numbers which come just after :
(a) 30 ________ (b) 50 ________
(c) 70 ________ (d) 95 ________
9. Write the factors, count the number of factors and then identify prime and composite numbers.
Number Factors Number of
Factors Prime or Composite
1 1 1 Neither Prime nor
composite
2
3
4
7
8
13
14
17
27
32
37
41
63
70
- 18 -
10. To see whether a number between 1 and 100 is prime or composite, we test divisibility by 2, 3 5 and 7. If the number is divisible by any of these then it is a composite number and if it is not divisible by 2, 3, 5 or 7 , then it is a prime number. Write P for the prime numbers and C for the composite numbers.
3 ______ 29 ______ 53 ______ 43 ______
12 ______ 34 ______ 68 ______ 54 ______
11. Circle all those numbers which are factors of 144 – (check by dividing)
5 9 6 8
12 2 10 3
144 36 52 72
16 13 100 0
12. Circle all the factors of 53
5 2 9 1
10 50 3 11
13 0 53 23
15 106 212 21
13. Circle the even numbers and put a square around the odd numbers.
5, 12, 144, 190, 545, 656, 59, 111, 400, 863
- 19 -
ACTIVITY
FINDING COMMON FACTORS & HCF
Colour the factors of each number in different colors and note the common factors.
HCF = _____________
HCF = _____________
HCF = _____________
HCF = _____________
Factors of 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Factors of 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Factors of 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Factors of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Factors of 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Factors of 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20
Factors of 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20
Factors of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 20
Factors of 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Factors of 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
- 20 -
ACTIVITY
SIEVE OF ERATOSTHENES TO FIND PRIME NUMBERS BETWEEN 1 AND 100
(a) Circle 2 and cross out all other multiples of 2. (b) Circle 3 and cross out all other multiples of 3. (c) Circle 5 and cross out all other multiples of 5. (d) Circle 7 and cross out all other multiples of 7. (e) Circle all the remaining numbers which are not crossed. They are all the prime
numbers from 1 to 100. (f) All numbers that have been crossed (except 1) are composite numbers.
1 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
14. Fill in the blanks using the prime number chart above:
(a) There are ________ prime numbers between 1 and 100.
(b) There are ________ prime numbers between 1 and 50.
(c) All the prime numbers between 1 and 100 are
_______________________________________________________________
(d) The smallest prime number is _______.
(e) The prime number which is even is __________.
(f) The smallest odd prime number is __________.
(g) The smallest composite number is __________.
(h) The smallest odd composite number is ___________.
2
- 21 -
(i) All prime numbers are odd except ___________.
(j) The pair of prime numbers which have a difference of 1 between them is _____.
(k) The greatest prime number less than 50 is ___________.
(l) The greatest prime number less than 100 is __________.
(m) The prime number just less than 20 _________________.
(n) Seven consecutive composite numbers with no prime number in between are
_____________________________________________________________.
(o) Prime numbers have only __________ factors.
(p) __________ is the smallest 2-digit prime number.
(q) Write 8 as the sum of two prime numbers. 8 = _____ + ______
(r) The smallest number you must add to 25 to make it a prime number is ______.
(s) Write all prime numbers less than 20. ________________________________
(t) Write all prime numbers between 40 and 60. ___________________________
(u) The sum of all prime numbers between 1 and 20 is _________.
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Playing with Numbers (Contd.)
Assignment 3B
1) A number is said to be divisible by another number when there is no _______________
2) A number is divisible by 3 if the __________________ is divisible by 3.
3) Fill in the blanks with the smallest possible digit so that the number is exactly divisible by 3
31__, 2042__, 30__0, 1__, 2__4
4) Find prime factorization of 72.
5) Find the pair of co-prime number: 6, 8; 8,9; 10, 21. (Give reasons)
6) Find prime factors of 54.
7) Find three common multiples of 2, 3 and 4.
8) Draw the factors trees of 80 and 45.
9) Find HCF of 12 and 30 by factor method.
10) Find HCF of 30 and 42 by common division method
11) Find HCF of 36 and 54 by prime factorization method.
12) Find HCF of 42 and 56 by long division method.
13) Find LCM of 6 and 9 by common multiple method.
14) Find LCM of 16 and 24 by prime factorization method.
15) Find LCM of 14 and 35 by common short division method.
16) Find the least number which when divided by 10, 14, 22 and 34 leaves remainder 5 in each
case.
17) Two buckets contain 18 litres and 24 litres of water. Find the maximum capacity of the
container which can measure the water of both the buckets when used in exact numbers of
times.
18) Find the least five-digit number, which leaves remainders 9 in each case when divided by 20, 40, 75.
19) The length, breadth and height of a hall are 3675 cm, 2100cm and 1050 cm respectively.
What can be the maximum length of a tape with which we can measure the length ,breadth and height of the hall?
20) Find the smallest number of 4 digits which is divisible by 6, 8, 9
21) What least value should be given to * so that the number 653*47 is divisible by 11 ?
22) What is the largest number of boys among whom 108 pencils and 180 eraser can be equally divided and what will be each boy's share?
- 23 -
23) Telegraph poles occur at equal distances of 220 metres along a road and heaps of stones
are put at equal distance of 300 m along the road. The first heap is at the foot of the first pole. How far down the road is the pole with a heap of stones at its foot.
ACTIVITY 1
1. Colour the box red if the number is exactly divisible by 9.
6111 2033 5724 4909 2034
307 166 5004 2241
2 Read each number in a part of the hexagon. Colour each portion in the following manner
– numbers divisible by 2 (Red); numbers divisible by 3 (Blue) and numbers divisible by 5
(green)
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ACTIVITY 2 : HCF of two numbers
RESULT : The HCF of two or more given numbers is the greatest among all their common
factors. Hence, Common Factors are 1, 2, 3, 6
Highest Common Factor = HCF = 6.
HCF by FACTOR METHOD (use different colours to write factors of different factors)
Common Factors of 36 & 60 are - ……………
Highest Common Factor of 36 & 60 = …….…
Common Factors of 44 & 66 are - ……………
Highest Common Factor of 44 & 66 = …….…
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ACTIVITY 3 : Finding LCM of three numbers (Multiple Method)
METHOD: 1. Let red colour represent the multiples of 4. Color first circle red on all the multiples of 4.
2. Let blue colour represent the multiples of 6. Color second circle blue on all the multiples
of 6.
3. Let green colour represent the multiples of 8. Color third circle green on all the multiples of 8.
4. Note down all the numbers where all the three circles have been coloured – red, blue, green.
5. You will note that the numbers are _____, ______, _____ and _____. 6. Out of these, _____ is the lowest (smallest) number. 7. _____ is the required LCM of the three numbers 4,6,8.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
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RESULT :
The Lowest Common Multiple of two or more numbers is the smallest among all their common
multiples. Hence, LCM of 4, 6 and 8 = ______
If Prime factorization of the given numbers is shown pictorially the HCF and LCM of the
numbers can be easily determined.
ACTIVITY 4 - Express the HCF and LCM of two numbers pictorially
(Prime factorization method)
Find HCF and LCM of 30 and 70 pictorially.
The shaded area shows HCF of two numbers. HCF = 2 x 5 = 10
The whole area shows LCM of two numbers. LCM = 3 x 2 x 5 x 7 = 210
Find HCF and LCM of 15 and 30
HCF of 15 and 30 = ……………………………….
LCM of 15 and 30 = ……………………………….
Prime
Factorisation
of 30
(……………..….)
Prime
Factorisation
of 45
(…………..…….)
Prime
Factorisation
of 30
(2 x 3 x 5)
Prime
Factorisation
of 70
(2 x 5 x 7 )
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ACTIVITY 5
Circle the flowers containing common factors of 20 and 40.
Circle the flower containing LCM of 5 and 6.
Circle the flower containing HCF of 7 and 8.
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Basic Geometrical Ideas
„Geo‟ means Earth and „metron‟ means Measurement.
POINT
1) The most basic shape in geometry is the Point.
2) A point determines a location.
3) A point has no dimensions (length, breadth or thickness).
4) A point is denoted by a single capital letter like A, B, C.
5) Examples of points are: the tip of a compass, the sharpened end of a pencil, the pointed end of a needle and a star in the sky.
LINE SEGMENT 1) A line segment has two end points.
2) A line segment is made up of unlimited points.
3) Examples of a line segment are: an edge of a box, a tube light, the edge of a post card.
4) A line segment is the shortest route between two points. The points are called the end
points.
5) A line segment has a fixed length. It does not have any thickness.
6) The symbol of a line segment is
7) A line segment is denoted by AB or BA. Both AB and BA denote the same line. LINE 1) A line segment is a part of a line. When a line segment from A to B (i.e. AB) is extended
beyond A in one direction and beyond B in the other direction without any end you get a model for a line.
2) A line has arrows at both ends as it can extend indefinitely in both directions.
3) The symbol of a line is .
4) It extends indefinitely in both directions and so it contains countless number of points.
5) A line is named using two capital letters for any two points on the line.
6) Sometimes a line is denoted by a letter like l, m.
7) Two lines can either meet at one point only or they will not meet at all.
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INTERSECTING LINES 1) If two lines have one common point, they are called intersecting lines.
2) Examples of intersecting lines are: two adjacent edges of your notebook, the letter X of the
English alphabet, crossing-roads.
3) Two lines can intersect only at one point.
4) More than two lines can also intersect in one point. PARALLEL LINES 1) Line segments which will not meet, however far they are extended are called parallel lines.
2) If two lines AB and CD are parallel, we write AB || CD.
3) If two lines l1 and l2 are parallel, we write l1 || l2..
4) Examples of parallel lines are: the opposite edges of ruler (scale), the cross-bars of a
window, the lines on a page of the Hindi notebook, rail lines.
RAY 1) Examples of a ray are: Beam of light from a light house, ray of light from a torch, sun rays.
2) A ray is a portion of a line.
3) It starts at one point (called starting point) and goes endlessly in a direction.
4) A ray is named using two capital letters. The first capital letter is the starting point of the ray
and the second capital letter tells the direction in which the ray is moving.
5) If PQ is the ray then its starting point is P and the point Q lies on the ray.
6) OB and BO are two different rays.
CURVES 1) A curve is any figure which can be drawn without lifting the pencil from the paper.
2) Even a straight line is considered to be a curve.
3) If a curve does not cross itself, then it is called a simple curve.
4) A curve is said to be closed if its ends are joined; otherwise it is said to be open.
5) In a closed curve, thus, there are three parts.
(i) interior („inside‟) of the curve (ii) boundary („on‟) of the curve and (iii) exterior („outside‟) of the curve.
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6) The interior of a curve together with its boundary is called its “region”.
POLYGONS 1) A polygon is a simple closed curve made up entirely of line segments. A polygon has at
least 3 sides.
2) The line segments forming a polygon are called its sides.
3) The sides of polygon ABCDE are AB, BC, CD, DE and EA.
4) The meeting point of a pair of sides is called its vertex.
5) Sides AE and ED meet at E, so E is a vertex of the polygon ABCDE.
6) The vertices of polygon ABCDE are A, B, C, D and E.
7) Any two sides with a common end point are called the adjacent sides of the polygon. The pairs of adjacent sides are AB and BC; BC and CD; CD and DE; DE and EA; EA and AB.
8) The end points of the same side of a polygon are called the adjacent vertices.
The pairs of adjacent vertices are: A and B; B and C; C and D; D and E; E and A
9) The joins of pairs of vertices which are not adjacent are called the diagonals of the polygon.
The diagonals are AC, AD, BD, BE, CE.
ANGLES
1) Angles are made when corners are formed.
2) When two rays have a common end point A, then two rays together are said to form an angle.
3) An angle is made up of two rays starting from a common end point.
4) The two rays forming the angle are called the arms or sides of the angle.
5) The common end point is the vertex of the angle.
6) To show an angle we use a small curve at the vertex.
7) Symbol for triangle is ∠.
8) To name an angle two points, one on each side and the vertex are used. Thus, ∠ POQ is a
better way of naming the angle instead of ∠ O.
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9) In specifying the angle, the vertex is always written as the middle letter.
10) The angle also has three parts associated with it, which are the interior, exterior and on the angle.
TRIANGLE
1) A triangle is a three-sided polygon.
2) It is the polygon with the least number of sides.
3) Symbol for triangle is
4) A triangle has three sides, three angles and three vertices.
5) Being a polygon, a triangle has an exterior and an interior.
6) In triangle ABC,
(a) The three sides of the triangle are AB , BC and CA .
(b) The three angles are ∠BAC, ∠BCA and ∠ABC.
(c) The points A, B and C are called the vertices of the triangle. QUADRILATERAL
1) A four sided polygon is a quadrilateral.
2) It has 4 sides, 4 vertices and 4 angles.
3) The vertices are named in a cyclic manner.
4) Quadrilateral ABCD has four sides AB, BC , CD and DA .
It has four angles ∠A , ∠B, ∠C and ∠D .
5) In any quadrilateral ABCD, adjacent sides are - and BC;
C and CD; CD and DA; and DA and AB.
6) Opposite sides are AB and DC ; and BC and AD.
7) Opposite angles are ∠A and ∠C; and ∠B and ∠D.
8) Adjacent angles are ∠A and ∠B; ∠B and ∠C; ∠C and ∠D; A and ∠D and ∠A.
9) Structures like electric towers make use of triangular shapes and not quadrilaterals as the triangle is very rigid and hence a strong shape. When we push inward at any one vertex of the triangle the triangle does not get distorted.
- 32 -
CIRCLE 1) A circle is a simple closed curve which is not a polygon.
2) Every point on the circle is at equal distance from the centre.
3) The radius is a line segment joining the centre to a point on the circle.
4) The plural of „radius‟ is radii.
5) The chord is a line segment connecting two points on a circle.
6) A line segment which connects two points on a circle and passes through the centre is
called the diameter.
7) Diameter is double the size of a radius.
8) All diameters are chords. The diameter is the longest chord of the circle.
9) An arc is a portion of circle.
10) A circle has three parts - the interior, exterior and on the circle.
11) A region in the interior of a circle enclosed by an arc on one side and a pair of radii on the other two sides is called a sector.
12) A region in the interior of a circle enclosed by a chord and an arc is called a segment of the circle.
13) The distance around a circle is its circumference.
14) A diameter of a circle divides it into two equal parts called semi-circle.
15) A semi-circle is half of a circle, with the end points of diameter as part of the boundary
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Basic Geometrical Ideas
Assignment 4
1) Name the following : (i) An area bounded by chord and major arc (ii) Each half equal part of the circle (iii) Longest chord of the circle (iv) The interior and boundary of a triangle (v) The common end point of an angle (vi) A set of points with one end point and can be extended in other direction (vii) A Figure having no length, breadth or height.
Lines which have a point in common. (ix) Lines which have no points in common. (x) The boundary of a circle (xi) Intersection point of two diameters of a circle (xii) A line which meets a circle at one point only (xiii) Simple. Closed figure made of line segments
2) Fill in the blanks: (i) Every _________________ has a definite length (ii) __________lines can be drawn that pass through two different points? (iii) All the Radii of circles are _________ (iv) The boundary of a circle is ca _______________. (v) There are ________ points on a line.
3) What are the symbols for the following : arc, line, parallel line.
4) If the diameter of a circle is 14 cm, then what is its radius?
5) How many radii can be drawn on a circle?
6) Name the points lying in the interior and exterior of DOE. Also name:
(i) Any three angles. (ii) The common Vertex (iii) The three rays
7) In the given figure
(i) Name the figure formed (ii) Name the three vertices (iii) Name the three sides (iv) Name the three angles (v) Name the side opposite to vertex A and (vi) Name the vertex opposite to the side opposite to AC
8) In the given quadrilateral MNOP identify.
(i) Two pairs of opposite sides (ii) Four pairs of adjacent sides (iii) 2 pairs of opposite angles (iv) 2 diagonals (v) Any two pair of adjacent angles
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9) The given figure is a circle with center „O‟. Identify (i) Radius(any four) (ii) Diameter of the circle (iii) 2 chords (iv) Sector of the circle (v) Segment of the circle.
10) Identify the closed curves from the following:
11) Identify the simple curves from the following:
12) Identify the polygons from the following figures.
13) Name all sides of the following polygon.
14) Name all vertices of the following polygon.
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15) Name all diagonals of the following polygon.
16) Consider the following figure. (a) Is it a curve? and (b) Is it not simple.
17) Name the angles of the following figure.
18) Identify the triangles from the following.
19) Identify the quadrilaterals from the following.
20) Write the names of all three triangles.
- 36 -
21) In the given quadrilateral MNOP identify: a) Two pairs of opposite sides. b) Four pairs of adjacent sides. c) 2 pairs of opposite angles. d) 2 diagonals. e) Any two pair of adjacent angles.
FUN WITH MATHS
ACTIVITY – FIGURE IT OUT
Look at the given figure and answer the following questions:
1. Number of radii
2. Number of chords
3. Name an arc
4. Name the longest chord
5. Sum of the angles in the nose of the figure
6. Shade a major segment
7. Colour two minor segments as red.
8. Name four collinear points.
- 37 -
ACTIVITY (CREATING CURVES WITH LINE SEGMENTS)
`1. Example:
2.
3.
- 38 -
4.
- 39 -
Understanding Elementary Shapes
Assignment 5
Fill in the blanks :
1. The distance between the end points of a line segment is its ___________________.
2. A graduated _______________ and a ___________________ are useful to compare
lengths of line segments.
3. When a hand of a clock moves from one position to another position we have an
example of an _______________________.
4. One full turn of the hand of a clock is 1 ___________________________.
5. A ______________________ angle is ¼ revolution.
6. A straight angle is _______________ revolution.
7. We use a _____________________ to measure the size of an angle in
____________________.
8. Turn 2 right angles from South. You will face _________________ direction.
9. The measure of an angle formed by two hands of a watch at 12:05 is _____________.
10. What fraction of a clockwise revolution does the hour hand of a clock turn through
when it goes from : (a) 9 to 6 (b) 7 to 10 (c) 6 to 12.
11. Where will the hand of a clock stop if it :
12. (a) starts at 12 and makes 1
2 of a revolution, clockwise.
(b) starts at 4 and makes 1
4 of a revolution, clockwise.
(c) Starts at 5 and makes 3
4 of a revolution, clockwise.
13. How many degrees are there in 2
5 of a straight angle.
14. How many degrees are there in 4 right angles .
15. How many degrees are there in 2½ right angles.
16. The measure of a right angle is _________________ and that of a ________________
is 180°.
17. An angle is ________________ if its measure is smaller than that of a right angle.
18. An angle is ________________ if its measure is greater than that of a right angle and
less than a _______________________ angle..
19. A _________________ angle is greater than a straight angle.
20. Two intersecting lines are _____________________ if the angle between them is 90°.
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21. The ________________________________ of a line segment is a perpendicular to the
line segment that divides it into two equal parts.
22. Triangles can be classified based on their angles :
Nature of angles in the triangle Name
Each angle is acute
One angle is a right angle
One angle is obtuse
23. Triangles can be classified based on the lengths of their sides:
Nature of sides in the triangle Name
All the three sides are of unequal length
Any two of the side are of equal length
All the three sides are of equal length
24. Polygons are named based on their sides:
Number of sides Name of the polygon
Three
Four
Five
Six
Eight
25. Quadrilaterals are classified with reference to their properties:
Properties Name of the Quadrilateral
Two pairs of parallel sides
Parallelogram with 4 right angles
Parallelogram with 4 sides of equal length
A rhombus with 4 right angles
26. A line segment is a fixed portion of a ______________.
27. 1 centimetre = _________ millimeters.
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28. 1 millimetre = __________ centimeters.
29. Sri Lanka is to the ______________ of India.
30. The four main directions are ___________, __________, __________ and _________.
31. The direction opposite to north is ________________.
32. If you stand facing north and turn clockwise by a right angle, you will face ___________
33. Turning by two ______________ angles you reach your original position.
34. The angle for one revolution is a ________________ angle.
35. The angle name for half a revolution is ______________________
36. The angle made by a ladder with the wall is ________________ angle.
37. A RA-tester is used to check ________________ angle
38. One complete revolution consists of __________ degrees
39. When two lines intersect and the angle between them is a right angle, then the lines
are said to be ______________________.
40. __________ is an English alphabet which illustrates perpendicularity.
41. the adjacent edges of a post card are models for ___________________ lines.
42. The opposite edges of a post card are models for __________________ lines.
43. A _____________ is a polygon with least number of sides.
44. If all the angles in a triangle are equal, then its sides are also _____________.
45. A polygon which has four sides is called a __________________.
46. A quadrilateral has _______ sides, ______ angles, _______ vertices and ______
diagonals.
47. In quadrilateral PQRS, the sides are ______, ______ , ______ and ______.
48. In quadrilateral PQRS, the angles are ________, ________ , ________ and _______.
49. In quadrilateral PQRS, the vertices are _______, _______, _______ and _______.
50. In quadrilateral PQRS, the diagonals are ________ and ________.
51. A quadrilateral in which two angles are right is a ______________________.
52. In the quadrilateral __________________ and _____________________ the diagonals
are perpendicular to each other.
53. The two types of set-squares in the instrument box are ______-______-_______ and
______-______-_______
54. The measure of each angle of a rectangle is ___________.
55. A figure is said to be ________________ if its sides are equal in length and angles are
equal in measure.
56. The name of the regular quadrilateral is __________________.
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57. The name of the regular triangle is __________________________.
58. The most useful shape in engineering constructions is the _________________
because of its sturdy nature.
59. Complete the table with yes or no:
Quadrilateral Opposite sides All sides
equal
Opposite
angles Equal
Diagonals
Parallel Equal Equal Perpendicular
Parallelogram
Rectangle
Square
Rhombus
Trapezium
60. The honey-comb of a bee is of ____________________ shape.
61. A __________________ is a line segment that joins any two vertices of the polygon
and is not a side of the polygon.
62. A rectangle has _____________ diagonals.
63. A cube is a ______________ dimensional shape.
64. Each side of the cube is a surface called a _______________.
65. Two faces of a cube meet at a ___________________ called an ______________.
66. _________________ edges of a cube meet at a point called _________________.
67. Each face of a cube has ____________ edges.
68. Each face of a cube has _____________ vertices.
69. A _________________ looks like a rectangular box.
70. A ________________ looks like a round pipe.
71. A ______________ looks like a „top‟ or the cap of a circus-clown.
72. A _______________ resembles a round marble used for playing.
73. A _______________________ is often the shape of a Kaleidoscope.
74. A road-roller is in the shape of a __________________.
75. In a _____________________ prism two of its faces (also called its base) is a triangle
and the other faces are _______________________________.
76. If the prism has a rectangular base, it is called a ______________________ prism.
77. Another name for a rectangular prism is ________________________.
78. Can a parallelogram be thought of as a rectangle?
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79. Three-dimensional shapes and the number of their faces, edges and vertices.
Shape Faces Edges Vertices
So a cube is just a special case of a square prism, and a square prism is just a special case of a rectangular prism.
And they are all cuboids.
80. A _________________ is a shape with a single base and the other faces are triangles.
81. A triangular pyramid is also called a ____________________________.
82. A pyramid with a square base and other faces are triangles is called a
______________ pyramid.
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83. A pyramid with a triangular base and other faces also triangles is called a
_________________ pyramid.
84. The _________________, the ______________ and the ________________ have no
straight edges.
85. The base of a cone is ________________________.
86. The cylinder has two bases which are in the shape of _______________.
87. A sphere has ________________ faces.
88. Can a quadrilateral have all the four angles acute? _______________
89. What fraction of a revolution clockwise does the hour hand of a clock turn through
when it goes from 8 to 5? ___________________
90. Where will the hand of a clock stop if it starts at 4 and makes ½ of a revolution
clockwise?
91. Which direction will you face if you start facing west and make ¾ revolution anti-
clockwise?
92. What part of a revolution have you turned through if you stand facing south and turn
clockwise to face east?
93. Find the number of right angles turned through by the hour hand of a clock when it
goes from 2 to 8.
94. How many degrees does the hour hand of a clock turn when it goes from 4 to 8?
95. How many right angles do you make if you start facing north and turn anti-clockwise to
east?
96. Where will the hour hand of a clock stop if it starts from 10 and turns through 2 right
angles?
97. Draw a rough sketch of a pentagon and draw its diagonals. How many diagonals are there?
98. Is a polygon? Why?
99. Into what figures does a diagonal divide a quadrilateral into?
100. Is a square a rectangle? Why?
- 45 -
FUN WITH MATHS
ACTIVITY - Tangram Cut out the square below into 7 shapes.
This is a very old Chinese puzzle known as a tangram. Cut out the 7 shapes and rearrange
them to form:
(a) a square from two triangles, and then change it to a parallelogram;
(b) a rectangle using three pieces, and then change it into a parallelogram;
(c) a trapezium with three pieces;
(d) a parallelogram with four pieces;
(e) a trapezium from the square, parallelogram and the two small triangles;
(f) a triangle with three pieces;
(g) a rectangle with all seven pieces.
Finally, put the pieces back together to form the original square.
- 46 -
Integers
Assignment 6
1. Represent the following by integers a. 7m above the sea –level b. Loss of Rs. 200 c. Withdrawal of Rs.700
2. Represent the following on a number line
i) 4 ii) – 5 iii) 0
3. Write all the integers between the given pair – 3 and 6 (Write them in increasing order)
4. Which is greater between – 8 and –10?
5. Which is the greatest negative integer?
6. Find the solution of the following using number line i) (-1) + 4
ii) (-2) + (-4) + 8
iii) (-2) + 7 + (-9)
7. Using number line write the integer which is 3 more than -2
8. If we are at –6 in number line, in which direction should we move to reach –1?
9. Arrange the following integers in decreasing order: - 4, 7, 0, -2, 3, -6
10. Fill in the Blanks with >, < or = sign. (-5) + (-8) _____ (-15) – (-2) 11. Find the sum of -315, 114 and –36
12. What is the solution for (–18) – (–18) + (–9) + (–3)?
13. Find the value (–8) – (–10)
14. What are the successor and predecessor of – 20?
15. What is the additive inverse of 89?
16. Which integer is equal to its additive inverse?
17. Which integer is 15 more than –55?
18. Find five pairs of integers such that sum of each pair is -7.
19. Fill in the blanks
(i) (-15) + ____ = 0 (ii) 73 + ____ = 0 (iii) -6 + ____ = 12 (iv) 15 + ____ = -8
20. What is the correct sequence of the numbers in ascending order?
- 47 -
(A) 0 < –1 < –2 (B) 1 < –1 < 0 (C) -1 < 0 < 1 (D) –2 < –3 < –4
21. What is the correct definition for integers? (A) A set of whole numbers (B) A set of whole numbers and natural numbers (C) A set of negative and natural numbers (D) A set of negative and whole numbers
22. Mohan traveled in a bus towards east of Delhi by 49 km and then towards the west of Delhi by 78 km. How far was he from Delhi finally?
23. For the statements, write true or False (i) The smallest integer is zero (ii) –18 is greater than –5 (iii) A positive integer is greater than its negative (iv) The successor of –297 is –298 (v) The predecessor of –193 is –194
24. Solve :
(i) 17 + 23 (ii) (–10) – 3 (iii) (– 75) + 18 (iv) 19 – (– 25) (v) 27 + (– 27) (vi) (– 20) + 0 (vii) (– 35) + (– 10) (viii) 7 – 9 (ix) 17 – (– 21) (x) (– 8) – (–14) (xi) (– 21) – (– 10) (xii) 32 – (–17) (xiii) (– 18) – (– 18) (xiv) (– 29) – 0
- 48 -
Fractions
Assignment 6
1) What fraction of the following figures is shaded?
2) Color in following fractions:
(i) 𝟐
𝟑 (ii)
𝟓
𝟖
3) Shade and find :
1. ½ of the collection
2. 1/3 of the collection
3. 2/3 of the collection
4. ¾ of the collection
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4) Write the following division as fractions :
(i) 4 ÷ 9 = ______________ (ii) 9 ÷ 19 = ______________
5) Write the following fractions as a division sum :
(i) 8
5 = ________ (ii)
7
3 = ___________
6) Write the following fraction in number form :
(i) One – tenth = _________ (ii) Ten – seventeenth = _________
(iii) Sixteen – twenty seventh = __________ (iv) Eleven – fortieth = __________
7) Write the following fractions in words :
(i) 8
3 = __________________ (ii)
19
17 = _________________
(iii) 34
15 = _________________ (iv)
115
111 = _______________
8) What fraction of a day is 12 hours?
9) Write the natural numbers from 4 to 15. What fraction of them are composite numbers?
10) Circle the proper fractions : 9
4,
9
8,
2
3,
10
1
11) Write each mixed number as an improper fraction.
12) Write each fraction as a mixed number or whole number.
13) Reduce to lowest term
18
36 =
80
140 =
35
235 =
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14) Complete the equivalent fractions:
8
12 =
32
1
2 =
8
4
10 =
90
15) Change the given fractions to like fractions:
(i) 5
8 ,
3
10 (ii)
2
9 ,
5
6 (iii)
1
5 ,
2
3,
3
4 ,
1
2
16) Compare the following:
(i) 3
4 ,
1
2 (ii)
8
9 ,
7
12 (iii)
1
5 ,
2
3,
3
4 ,
1
2 (iv)
4
15 ,
4
5 (v) 8
2
3 ,
27
4
17) Arrange in ascending order: 5
6 ,
7
8,
3
4 ,
4
9,
1
3
18) Find an equivalent fraction of 64
36 with denominator 32.
19) Write 5
8 with numerator 20.
20) Check whether 7
6 and
13
12 are equivalent or not.
21) Add the following fractions:
(i) 3
2 +
1
2 (ii) 1
3
8 + 4
2
8 (iii)
1
5 +
2
3 (iv) 2
1
2 + 1
4
5 (v) 4
2
3 + 3
22) Subtract the following fractions:
(i) 1 1
4 –
3
4 (ii) 1 –
5
8 (iii)
4
5 –
2
3 (iv) 2 – 1
4
5 (v) 4
2
3 – 3
1
4
23) Naina bought a plant that was 42
3 cm tall. In the first week, it grew 1
5
8 cm and the next
week it grew 3 1
2 cm. Now how tall is Naina‟s plant?
24) Rashmi bought 3
4 metre of cloth and Madhu bought
3
5 metre of cloth. Who bought more
cloth and by how much?
25) Joginder was given 3
8 of a basket of apples. Vinod got
1
3 of the basket. The rest of the
basket was given to Amit. What fraction of the basket was given to Amit?
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26) Saransh purchased books worth Rs. 65 3
4 and gave Rs. 100 to the shopkeeper. Find the
amount of money returned by the shopkeeper.
27) A teacher taught 3
5 of a book, sunny revised
1
5 more on his own. How much does he still
have to revise?
28) Seeta exercised for 1
2 of an hour, while Geeta exercised
3
5 of an hour. Who exercised for
a longer time?
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Decimals
Assignment 8
1) Do as directed :
(i) Write 7 cm 5 mm as cm (using decimal)
(ii) Fill in the blank : 5.05 _____ 5.5 (Put <, > or =)
(iii) Express „5 tenths 4 hundredths‟ as a decimal number
(iv) Among 0.5, 0.05, 5.5, 0.005, which is the smallest?
(v) Find the value of 2 - 0.7
(vi) 0.47 lies between which two tenths?
(vii) Write the following number as Decimal : Two hundred five and three tenths.
2) Fill in the blanks:
(i) Decimal notation of 500 + 3 + 7
10 +
4
1000 is ________.
(ii) Decimal form of „Eleven point two three five‟ is ______.
(iii) 5454 m= _________km
(iv) Lata spent Rs 9.50 for buying a pen and Rs 2.50 for one pencil. She spent Rs.
__________ in all.
(v) 1.73 has ________ places of decimal.
(vi) Decimal number 21.015 written in words is _______________________
(vii) 13.9 lies between two whole numbers, _____and_______ and it is closer to ________
whole number on the number line.
(viii) Write 12.5 as a fraction in lowest form.
(ix) Convert 3
25 into decimal
(x) Write 450 gms as kilograms
3) Answer the following questions:
(i) Write 0.125 as fraction in lowest terms.
(ii) Write 18.053 in the place value table
(iii) Show 1.2 on number line.
(iv) Find the sum of 280.04 + 28.5 + 19
(v) Find the difference : 17 – 4.683
(vi) Which is greater in 5.64 and 5.603?
(vii) On the given number line above, which decimals do the following points A, B, C, D, E
represent?
4) A milkman has 25 litres 50 ml of milk. He gives 8 litres 250 ml to one customer and 12 litres
100 ml to another customer. How much milk does he have now?
5) Ritu‟s school is at a distance of 6 km 530 m from her home. She traveled 1 km 70 m by foot
and rest by bus. How much distance did she covered by bus?
6) Shanti had 25 m 5 cm long cloth. She cuts 8 m 25 cm length of cloth from this for making a curtain. How much cloth is left with her?
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ACTIVITY
Decimals Crossword Puzzle
1
2
3
4
5 6
7 8 9
10
11 12
13
14
HINTS ACROSS
2) 89.97 – 72.26 = _______________
3) 5.12 – 2.1 = _______________
4) 256
25 in decimal form = _______________
5) 93.24 – 8.234 = _______________
7) 1234.432 + 1.08 = _______________
11) 88.30 + 72.48 - 22.54 = _______________
13) 400 + 80 + 6 + 6
10 +
7
100 +
4
1000 = _______________
14) 134.42 + 0.88 + 340.002 = _______________
DOWN 1) Twenty-three, four tenths, eight hundredths = _______________
2) 88.88 – 22.22 + 55.55 = _______________
6) Rs 6307, 23p + Rs 518, 4p = _______________
8) Rs. 5128, 73p in decimal form = _______________
9) 207 kg 52 g in decimal form = _______________
10) 6.14 – 3.1 = _______________
12) 55.38 – 24.83 = _______________
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Data Handling
Assignment 9
1) The collection of facts, figures, numbers etc. is called......
2) Fill in the blanks : The number represented by tally marks is_____. 3) Fill in the blanks: Pictograph represents data in form of ____
4) There are 25 students in class VI. Represent the number of students by tally marks.
5) On the basis of given information answer the following question. Draw a frequency table
using tally marks. Final marks of 20 students are as follows: 53, 61, 48, 60, 78, 68, 55, 100, 67, 90, 75, 88, 77, 37, 84, 58, 60, 48, 62, 56 If 40 is the pass mark how many have failed?
6) In a Mathematics test, marks obtained by the 40 students are as follows, arrange them in a table by using the tally marks.
8 1 3 7 6 5 5 4 4 2
4 9 5 3 7 1 6 5 2 7
7 3 8 4 2 8 9 5 8 6
7 4 5 6 9 6 4 4 6 6
Also find: (a) How many students obtained maximum marks. (b) How many students obtained minimum marks. (c) How many students obtained marks more than 4.
7) The following pictograph shows the number of students of class VI in a school, using the
different means of transport to travel to school.
Find: (a) Number of Students coming by Car. (b) The Most Popular way of traveling used by the students. (c) Which means of transport is used by the minimum number of students (d) How many students are using the transport other than Car, School Bus, Cycle.
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8) The colour of clothes liked by the students of class VI in a school is shown by pictograph
Color ☺=10Students
Red ☺ ☺ ☺ ☺
Yellow ☺ ☺ ☺
Blue ☺ ☺ ☺ ☺ ☺ ☺ ☺
White ☺ ☺
i) Find the number of students who liked blue colour
ii) How many liked yellow colour?
iii) Which is the most favorite colour?
iv) How many students are there in this class?
9) Draw the pictograph, Number of students‟ presents in a class of 40 students during a week.
Day Number of Students present
Monday 24
Tuesday 28
Wednesday 36
Thursday 32
Friday 32
Saturday 24
10) Following are the details of number of students present in a class of 40 students during a
week. Draw the pictograph for this information.
Days Number of students present
Monday 24
Tuesday 28
Wednesday 36
Thursday 32
Friday 32
Saturday 24
11) Read the bar graph shown in the figure and answer the following question:
What is the number of students wearing shoe no. 6?
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12) Given Bar-Graph , represent the amount of oil purchased by the government from 1998-2005. Read the Graph and give your observation under following topics:
a) In which year was maximum oil purchased ? b) In which year was minimum oil purchased ?
13) The data below represents the number of Maths books sold by a shopkeeper in six days. Draw a bar graph to represent the above data.
Days Number of books sold
Monday 60
Tuesday 40
Wednesday 30
Thursday 50
Friday 30
Saturday 60
14) The number of chemistry books sold by a shopkeeper on six consecutive days is shown
below:
Days Sunday Monday Tuesday Wednesday Thursday Friday
Number of books sold
65 40 30 50 20 70
What is the total number of books sold in the six consecutive days?
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Mensuration
Assignment 10
1) Calculate the perimeter.
(i) (ii) (iii)
2) Find the perimeter of Square whose side is 13cm
3) Find Area of a Square of whose length is 1 unit.
4) Find the perimeter of a regular hexagon with each side measuring 8m.
5) Find the perimeter of a rectangle whose length and breadth are 25 cm and 15 cm respectively.
6) The area of rectangle is 225 cm2, its breadth is 25cm find, its length.
7) Find the perimeter of a rectangle whose area is 650 cm2 and its breadth is 13cm.
8) Find the perimeter of an isosceles triangle with equal sides 8 cm each and third side is 6cm.
9) How many times will the area of a rectangle increase if its length is doubled and breadth is tripled?
10) One side of a square field is 300m. Find the cost of leveling it. If the rate for leveling is Rs 5 per m2?
11) Find the perimeter of an equilateral triangle of side 9cm.
12) A marble tile measures 25 cm by 20 cm. How many tiles will be required to cover a wall of size 4m by 3m?
13) Find the cost of fencing a rectangular park of length 300 m and breadth 200 m at the rate of Rs. 24 per metre.
14) Find the area of square whose side is 5 cm.
15) Find the breadth of the rectangle whose perimeter is 360 cm and whose length is 100 cm
16) Find the perimeter of a square whose side is 5 cm
17) Find the side of a square whose perimeter is 100 cm
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18) Find the cost of fencing a square park of side 300m at the rate of Rs 20 per metre.
19) A rectangle has the area equal to that of a square of side 80cm. If the breadth of the
rectangle is 20cm, find its length.
20) What is the perimeter of a regular pentagon with each side measuring 4 cm.
21) The perimeter of a regular pentagon is 50 cm. How long is its each side?
22) Find the side of a square whose perimeter is 40 m.
23) Two sides of a triangle are 12 cm and 15 cm. The perimeter of the triangle is 40 cm. What is the length of its third side?
24) A floor is 5 m long and 5 m wide. A square carpet of sides 4 m is laid on the floor. What is the area of the floor that is not carpeted
25) The perimeter of a square is 16 cm. What is the area of square?
26) The area of a rectangle is 42 sq. cm. If breadth of the rectangle is 6 cm, what is its perimeter?
27) Q 62 Find the area of figure.
28) A hall in the form of a rectangular region is 14m by 12 m. How may marbles slabs 8cm by 6 cm are needed to cover the floor of the hall.
29) A rectangular metal plate is 5dm4cm long and 4dm3cm wide. If the metal cost is Rs. 75 per sq m, find the cost of the plate.
30) Q 66 How may rectangle be able to drawn with 36cm as the perimeter, given that the side is
positive integers in cm?
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Algebra
Assignment 11
1) How are the following expressions formed? (i) a + b (ii) -3q (iii) 2n – 1
(iv) 𝑥
3
(v) 3 x + 2
2) Give expressions for the following : (i) 5 less than a number x
(ii) Decrease x by 7
(iii) Subtract 4 from x
(iv) X less than the sum of y and 7
(v) Decrease the sum of x and y by z
(vi) Three times x added to y
(vii) 3 times x subtracted from y
(viii) 5 more than thrice a number x
(ix) 3 times x added to 7 times y
(x) Quotient of x by 4 added to y
(xi) Quotient of z by 6 multiplied by y
(xii) 3 taken away from the quotient of x by 3y.
3) Write the equation for the following:
(i) The diameter of a circle is twice its radius
(ii) The area of a rectangle is the product of its length and breadth.
(iii) Selling price equals the sum of the cost price and the profit.
(iv) The amount equals the sum of the principal and the interest.
(v) The perimeter of a rectangle is two times the sum of its length and breadth.
(vi) The perimeter of a square is four times its side
(vii) The associative property of addition of whole numbers.
(viii) The distributive property of multiplication over addition of whole numbers.
4) Change the following statements using expressions into statements in ordinary
language.
(a) Tony puts q marbles on the table. He has 8 q marbles in his box.
(b) Our class has n students. The school has 20 n students.
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5) Write expressions for the following situations (a) Sarita has 10 more marbles than Ameena. Let Ameena have x marbles. (b) Balu is 3 years younger than Raju. Let Raju‟s age be x years. What is Balu‟s age? (c) Bikash is twice as old as Raju. What is Bikash‟s age. (d) Raju‟s father‟s age is 2 years more than 3 times Raju‟s age. What is his father‟s
age? (e) How old will Susan be 5 years from now, if she is x years old now? (f) How old was Susan 4 years ago? (g) Price of wheat per kg is Rs 5 less than price of rice per kg. (h) Price of oil per litre is 5 times the price of rice per kg. (i) The speed of a bus is 10 km/hour more than the speed of a truck going on the same
road.
6) Find the rule that gives the number of matchsticks
7) Find a rule to give the number of matchsticks required to make a pattern of Ls.
8) Write the rule for the perimeter of a square, using variables.
9) Which out of the following are expressions with numbers only? (a) y + 3 (b) (7 × 20) – 8z (c) 5 (21 – 7) + 7 × 2 (d) 5
10) Form expressions using t and 4. Use not more than one number operation. Every
expression must have t in it.
11) Write the rule for perimeter of the rectangle
12) Write the rule for Distributivity of numbers
13) Write the expression for the following: (i) Anjali scores 100 marks in Mathematics and x marks in Science. What is her
total score in Science and Mathematics?
(ii) The score of Ishita in Mathematics is 25 more than two thirds of her score in science. If she scored x marks in science, determine her score in Mathematics.
(iii) John covers x centimeters in one step. How many centimeters does he cover in 9 steps?
(iv) Rohan spends Rs x daily and saves Rs y per week. What is his income after 3 weeks?
The diameter of a circle is a line which joins two points on the circle and also passes through
the centre of the circle. In the adjoining figure AB is a diameter of the circle and C is the centre.
Express the diameter of the circle (d) in terms of its radius (r).
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Ratio and Proportion
Assignment 12
1. Which of the following represents the ratio notation: (i) a + b (ii) a – b (iii) a : b (iv) a.b
2. Find three equivalent ratio of 8 : 5
3. Find the ratio of 40 paise to Rs.2
4. Amita and Vinita have Rs. 128 and Rs. 192 respectively. Express the amounts they have
as a ratio in the simplest form
5. Find the ratio of 20 seconds to 20 minutes
6. A swimming team consists of 12 boys and 9 girls. What is the ratio of : a) Boys to girls b) Boys to total number of members in the team c) girls to boys d) Girls to total number of members in the team.
7. Verify whether the ratio are in proportion or not?
(i) 2 : 1 and 50 : 25
(ii) 25 : 75 and 5 : 3
(iii) 42 : 7 and 12 : 14
8. Divide Rs. 120 between Saroj and Sonal in the ratio 3 : 5.
9. Find the ratio of 40 cm to 2.5 m.
10. In a box containing 80 bulbs, 15 were found to be defective. Find the ratio of defective to good bulbs.
11. Pradeep and Suresh bought a bat for Rs. 250. Pradeep paid Rs. 175 and Suresh paid the rest. What is the ratio of the amount Pradeep paid to the amount Suresh paid?
12. The price of bread increased from Rs. 12 to Rs. 13. Find the ratio of the increase in price to the original price.
13. The membership fee of a club is increased from Rs. 980 to Rs. 1000 per month. Find the ratio of the increased fee to the original fee.
14. Sunita gets Rs. 500 per month as her pocket money. Out of which she saves Rs 40 per month. Find the ratio of her savings to the amount she gets.
15. Divide Rs. 150 between Abhishek and Anil in the ratio 3 : 7.
16. Divide Rs. 225 between Kanchan and Riya in the ratio 7 : 8.
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17. Sumit buys pencils at the rate of Rs 6 per dozen and sells them at the rate of Rs. 13 per dozen. What is the ratio of :
a) cost price to selling price b) profit to selling price c) cost price to profit d) selling price to cost price.
18. In a sports meet, groups of boys and girls are to be formed. Each group consists of 4
boys and 6 girls. How many boys are required, if 102 girls are available for such groupings.
19. Out of 1800 students in a school, 750 opted football, 800 opted cricket and remaining opted hockey. If a student can opt only one game, find the ratio of :
a) The number of students opting football to the number of students opting cricket. b) The number of students opting football to the number of students opting hockey. c) The number of students opting cricket to the total number of students.
20. The length and breadth of a rectangle are in the ratio 5 : 4. if its length is 80 cm, find the
breadth.
21. A bus travels 205 km on 20 litres of petrol. How much petrol will be needed to cover a journey of 369 km?
22. If 12 boxes are required to hold 48 litres of milk, then (a) How many boxes will be required to hold 60 litres of milk. (b) How many litres of milk will there be in 36 boxes?
23. Amita and Vinita have Rs. 128 and Rs. 192 respectively. Express the amounts they have as a ratio in the simplest form.
24. Determine if the following are in proportion - 32, 48, 140, 210. If they are then write down the middle terms and the extreme terms.
25. The ratio of the boys to girls in a school is 7: 6. If there are 24 girls then find the total number of students in the class.
26. There are 24 balls in a bag. Of them there are 14 white balls ,and the remaining are red. Find the ratio of (i) Number of white balls to total Number of balls (ii) Number of white balls to Number of red balls
27. 100 gm of butter makes 14 cakes. How many cakes will 150 gm make?
28. A plane flies 405 km on 90 litres of fuel. How much fuel is needed for 540 km? How far
can it go in 50 litres?
29. 16 articles cost Rs. 72. What will be the cost of 30 articles? How many articles can be
bought for Rs. 207?
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30. A journey of 552 km takes 6 days. How long will a journey of 1012 km take, if it is done
at the same rate?
31. Harsh takes 150 steps in walking a distance of 125 metres. What distance would he
cover in 360 steps? How many steps would be needed to cover a distance of 120m?
32. A farmer sells 40 quintals of rice for Rs. 20000. What quantity of rice would he sell in
order to receive Rs. 24000?
33. Cost of 3 geometry boxes is Rs. 33. How many geometry boxes can be bought for Rs.
121?
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Symmetry
Assignment 13
1. Give two examples having only one line of symmetry. Draw their figures and mark their line of symmetry.
2. Give two examples having exactly two lines of symmetry. Draw their figures and mark their lines of symmetry.
3. Draw the lines of symmetry of the following (a) Rectangle (b) Equilateral triangle (c) Square (d) Circle
4. Classify the following alphabets into horizontal and vertical line of symmetry: A, B, C, D,E, H, I, K, M, N, U, V.
5. Draw the other part of the figure to make them symmetrical :
6. Draw a triangle having (i) no line of symmetry, (ii) one line of symmetry, (iii) three lines of symmetry.
7. Draw a quadrilateral having
(i) no line of symmetry, (ii) one line of symmetry, (iii) two lines of symmetry, (iv) four lines of symmetry.
8. State „true‟ or „false‟:
(i) Letter H has neither vertical nor horizontal line of symmetry. (ii) A ring has only one line of symmetry. (iii) Medians of an equilateral triangle are its lines of symmetry. (iv) Letter C does not have mirror symmetry. (v) Letter V has only vertical line of symmetry.
9. State „true‟ or „false‟:
(i) Letter H has neither vertical nor horizontal line of symmetry. (ii) A ring has only one line of symmetry. (iii) Letter C does not have mirror symmetry. (iv) Letter V has only vertical line of symmetry. (v) A parallelogram has two lines of symmetry.
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10. Some symmetrical figures are given. Draw the line of symmetry in each of these:
j. k. l. m.
11. Draw the following :
(i) With respect to a horizontal mirror, draw the mirror image of five alphabets having Reflection symmetry and 5 alphabets which do not have Reflection symmetry.
(ii) With respect to a horizontal mirror, draw the mirror image of five alphabets having Reflection symmetry and 5 alphabets which do not have Reflection symmetry.
(iii) Name three alphabets that have: a) Reflection symmetry along both horizontal and vertical mirrors b) no reflection symmetry
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12. Draw the lines of Symmetry in the following 2D shapes
Equilateral Triangle Isosceles Triangle Square
Rhombus Rectangle
13. Find the mirror image with respect to the given mirror line and colour following figures.
Also, show the line of symmetry with a different colour.
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Practical Geometry
Assignment 14
1) Construct the following angles using protractor: (i) 78° (ii) 136° (iii) 94°
2) Draw a circle of radius 3.2 cm.
3) With the same centre O, draw two circles of radii 4 cm and 2.5 cm.
4) Draw any circle and mark points A, B and C such that (a) A is on the circle. (b) B is in the interior of the circle. (c) C is in the exterior of the circle.
5) Let A, B be the centres of two circles of equal radii; draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether AB and CD are at right angles.
6) Draw a line segment of length 7.8 cm using a ruler.
7) Construct a line segment of length 6.6 cm using ruler and compasses.
8) Construct AB of length 8.8 cm. From this, cut off AC of length 4.9 cm. Measure BC .
9) Given AB of length 3.9 cm, construct PQ such that the length of PQ is twice that of AB. Verify by measurement.
10) Given AB of length 7.3 cm and CD of length 3.4 cm, construct a line segment XY such that the length of XY is equal to the difference between the lengths of AB and CD. Verify by measurement.
11) Draw any line segment PQ. Without measuring PQ, construct a copy of PQ. Given some line segment AB, whose length you do not know, construct PQ such that the length of PQ is twice that of AB.
12) Draw any line segment AB. Mark any point M on it. Through M, draw a perpendicular to AB. (use ruler and compasses)
13) Draw any line segment PQ. Take any point R not on it. Through R, draw a perpendicular to PQ. (use ruler and set-square)
14) Draw a line l and a point X on it. Through X, draw a line segment XY perpendicular to l. Now draw a perpendicular to XY at Y. (use ruler and compasses)
15) Draw AB of length 7.5 cm and find its axis of symmetry.
16) Draw a line segment of length 8.5 cm and construct its perpendicular bisector.
17) Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.
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18) Draw a circle with centre C and radius 3.4 cm. Draw any chord AB. Construct the perpendicular bisector of AB and examine if it passes through C.
19) Draw an angle of measure 147° and construct its bisector.
20) Draw a right angle and construct its bisector.
21) Construct with ruler and compasses, angles of following measures: (a) 60° (b) 30° (c) 90° (d) 120° (e) 45° (f) 135°
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Sample Paper – PT1
Ques 1) Answer the following questions : (9 x 1 = 9 marks)
(i) Round off 7695 to nearest thousands
(ii) Write the number in numerals : Fifty six crores, nine lakh, eight thousand and
fifteen
(iii) Write 90,00,000 + 40,000 + 3000 + 20 + 6 as a numeral
(iv) How many thousands make a million?
(v) How many numbers exist between 51 and 100?
(vi) Write 996 as Roman Numeral
(vii) Write CDLXXXIV as Hindu-Arabic numeral
(viii) Write the greatest 5-digit number having three different digits.
(ix) Round off 12,096 to the nearest tens.
Ques 2) Form the following numbers : (2 x 2 = 4 marks)
a) Write all possible three digit numbers using the digits 6,0,4 when repetition of the
digits are not allowed.
b) Make the greatest and the smallest 4-digit numbers using any four different digits
with digit 9 always at tens place.
Ques 3) Do as directed : (2 x 3 = 6 marks)
a) Name the following :
(i) Triangle having no line of symmetry
(ii) Number of lines of symmetry in a circle
(iii) An alphabet having both horizontal and vertical lines of symmetry
b) Give an example and draw for each :
(i) Number which can be shown as square
(ii) Number which can be shown by two different rectangles
(iii) Number which can be arranged as triangle
Ques 4 Do as directed : (8 x 2 = 16 marks)
a) Solve the following, using BODMAS rule : 9 + 6 ÷ 2 x 9 – 3 + 1
b) Find the sum by suitable rearrangement: 2619 + 354 + 8381 + 746
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c) Draw the mirror image of B along horizontal and vertical mirror lines
d) Find the product by suitable rearrangement: 8 × 192 × 125
e) Find the value of the following, using suitable properties : 529 × 92 + 8 × 529
f) Find the product using suitable properties : 837 × 102
g) Give an estimate (by rounding off to the nearest hundreds) for 538 + 234 + 4,318
h) Estimate the product of 97 × 318 using general rule
Ques 5 Solve : (5 x 3 = 15 marks)
a) (i) Write the number 191560050 in words, according to Indian system of
numeration.
(ii) Write the number 507476123 in words, according to International system of
numeration.
b) The monthly fee for a student in a school is Rs.310. If there are 620 students in the
school, find the total monthly collection of fees.
c) A taxidriver filled his car petrol tank with 30 litres of petrol on Monday. The next day,
he filled the tank with 70 litres of petrol. If the petrol costs Rs 64 per litre, how much
did he spend in all on petrol?
d) In a town there are 45679 men, 39842 women and 24056 children. Find the total
population of the town?
e) The distance between the park and house of a student is 1Km 275m. Every day he
walks both ways between the park and his house. Find the total distance covered by
him in a week’s time?
**********************
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SAMPLE PAPER PERIODIC TEST– II
General Instructions 1. All questions are compulsory. 2. This question paper consists of 30 questions divided into four sections - A, B, C & D 3. Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains of 4 marks each.
SECTION A ( 1 mark each) Q: 1 Write the greatest 5 digit number which can be formed by using digits 7, 5, 3 and 2 Q: 2 Write the successor of the greatest 3 digit number. Q: 3 Write all the factors of 20 Q: 4 What is the name given to the longest chord of a circle ? Q: 5 Write two numbers that can be arranged as triangle. Q: 6 How many lines of symmetry are there in a rectangle? SECTION B ( 2 marks each)
Q: 7 Solve the following using BODMAS rule 8 + 24 ÷ 3 X 2 – 1 Q: 8 Find the sum of the following using suitable rearrangement
1983 + 647 + 217 + 353 Q: 9 Draw number line and locate the following points on it.
1
2,
1
4 ,
3
4 ,
4
4
Q: 10 Using the number line, Add the following 5 + (– 11 )
Q: 11 Subtract (– 65 ) from (– 110 )
Q: 12 Rohan had 30 apples with him. He gave 20 apples to his elder brother. What fraction of apples is left with Rohan? SECTION C ( 3 marks each) Q: 13 Using the divisibility test, Check whether the number 3439172 is divisible
by 11 or not ? (show the working )
Q: 14 Find the L.C.M of 12, 16 and 24
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Q: 15 A taxi driver filled his car petrol tank with 40 litres of petrol on Monday. The next day, he filled the tank with 50 litres of petrol. If the cost of petrol is Rs 44 per litre. How much did he spend all in petrol?
Q: 16 (a) Insert commas and write the number 234637 according to Indian system of numeration. (b) Insert commas and write the number 2856721 according to
International system of numeration.
Q : 17 Find the H.C.F of 30 and 42
Q: 18 Rahul read 25 pages of a book containing 100 pages and sumit read 2
5 of
the Same book. Who read less ?
Q: 19 From the given figure, name the following:
(a) Two lines containing point E
(b) Two pairs of intersecting lines
(c) Line on which point O lies
Q: 20 Fill in the blanks with appropriate Sign: ( ‘<’ , ‘>’ or ‘=’ )
(a) 1
2 □
1
5 (b)
12
24 □
21
42 (c)
3
4 □
2
8
Q : 21 How many possible lines of symmetry are in the following figure.
(a) (b) (c)
Q : 22 Find (a) (– 13) – (– 8) – ( +10 ) (b) (– 7 ) + (– 9) – ( –16)
SECTION D ( 4 marks each)
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Q: 23 Draw any circle. Mark and name the following: (a) its centre (b) a chord (c) a segment (d) a sector
Q: 24 (a) Find the value of 5427 X 92 + 8 X 5427 using suitable properties.
(b) Find the product of 125 X 40 X 8 X 25 using suitable rearrangement
Q: 25 (a) Estimate the sum of 17,986 and 5290 using general rule (b) Find the difference between the greatest and least number that can be written using the digits 6 , 2 , 7, 4 ,3 each only once.
Q: 26 Determine the greatest 3 digit number exactly divisible by 8 , 10 and 12 , Q: 27 (a) Draw any open curve made up entirely of line segment. (b) Name two alphabets having only vertical line of symmetry. (C) Name and draw a triangle having three lines of symmetry. (d) Draw a quadrilateral PQRS and name its two diagonals.
Q: 28 Find the sum of the following: (a) 37 + (– 2) + (– 65) + (– 8) (b) (– 63) – (– 10) + 28 + ( – 7)
Q: 29 (a) Express 15
4 as mixed fraction
(b) Write fraction equivalent to 3
4 with denominator 16
(c) Reduce 42
68 to simplest form
(d) Express 16 2
3 as improper fraction
Q: 30 Solve :
(a) 2
3 +
3
7 (b)
45 –
2
3
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Sample Paper – PT3
SECTION A
(Question numbers 1 to 5 carry one mark each)
1) Write ‘Five and twenty-five thousandths’ as a decimal.
1
2) Write as a decimal : 100 + 9 + 9
100 +
1
1000
1
3) 0.91 lies between which two tenths?
1
4)
a)
b)
Fill in the blanks using >, < or =
1.234 ______ 12.34
5.05 ______ 5.50
1
5) Write 14
5 as a decimal.
1
SECTION B
6)
a)
b)
c)
d)
Fill in the blanks with appropriate answers:
405 paise = Rs___________
3 cm 6 mm = ___________ cm
8223 m = ___________ km
4 kg 44 g = ___________ kg
2
7)
a)
b)
If represents 8 bulbs, then
represent __________ bulbs.
_______________ represent 24 bulbs.
2
8) The area of a rectangle is 40 sq.cm. If its breadth is 4 cm, then what is its
length.
2
9) The length and breadth of a rectangle are 18 m 50 cm and 13 m respectively.
What is its perimeter?
2
10) A string is 42 cm long. It is used to make a regular hexagon. What will be the
length of each side of the hexagon?
2
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SECTION C
(Question numbers 11 to 15 carry three marks each)
11) a)
b)
If perimeter of a square is 48 cm, what is the length of its side?
Also find the area of the square.
3
12) How many tiles whose length and breadth are 12 cm and 5 cm respectively
will be needed to fit in a rectangular region whose length and breadth are 120
cm and 132 cm, respectively?
3
13) Pick out the solution from the values given in the bracket next to the equation.
Show that the other values do not satisfy the equation. : 2m + 3 = 7 (5, 1, 2)
3
14) a)
b)
c)
The side of a regular pentagon is denoted by ‘s’. Express the perimeter of the
pentagon using ‘s’.
Write how the expression has been formed : ‘2 y – 5’
Change the following statements using expressions into statements in
ordinary language: Jaggu is z years old. His uncle is 4z years old.
3
15) Urmila’s school is at a distance of 5 km 350 m from her house. She travels 1
km 70 m on foot and the rest by bus. How much distance does she travel by
bus?
3
SECTION D
(Question numbers 16 to 20 carry four marks each)
16) a)
b)
Rupesh takes three rounds of a field which is in the shape of an equilateral
triangle having length of each side as 35m. How much distance does he travel
in all?
The perimeter of an isosceles triangle is 23cm. If each of its equal sides are 9
cm, then what is the length of the third side?
4
17) Find the perimeter and area of the given shape:
4
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18)
a)
b)
c)
d)
Fill in the blanks: (write only the answer):
The expression for : ‘x multiplied by -5’ is ______________
The length of a rectangle is twice the breadth. If the breadth is x cms, then the
length is _______ cms.
Raghu is 4 years younger than 3 times Raju’s age. If Raju’s age is y years,
then Raghu’s age is ______ years.
If Pinky’s present age is ‘a’ years, her age 5 years ago was _________
4
19)
a)
b)
c)
Sheela rolled a dice twenty times and recorded her observations as follows
1,3,3,2,6,3,3,1,4,5,
2,6,6,3,4,5,4,6,1,3.
Make a table and enter the data using tally marks.
What is the minimum observation?
Which observation appears most number of times.
4
20) The number of students taking part in various games in a secondary school
are given below. Draw a bar graph for the given data.
Games Athletics Basket
Ball Net Ball Cricket
Foot
Ball Tennis
Number
of
Students
6 9 18 24 21 15
4
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Sample Paper – Annual Examination
SECTION A
(Question numbers 1 to 6 carry one mark each)
1) What type of angle is made by the minute hand of a clock when it moves from
10 to 4?
1
2) Find the area of a square whose side is 4 cm.
1
3) Find the perimeter of a regular Hexagon, if its each side measures ‘s’ cm.
1
4) Find the ratio of 20 cm to 1 m
1
5) 34 + ____ = -12
1
6) Write the integers for the following statements : Raj lost Rs 2000 in a business
deal.
1
SECTION B
(Question numbers 7 to 12 carry two marks each)
7) Pick out the solution from the values given in the bracket next to the equation
and verify your answer: x + 4 = 2 (– 2, 0, 2, 4)
2
8) Draw a line segment PQ = 8.5 cm. Take a point M above the line segment PQ.
Construct a perpendicular from M to PQ using scale and compass only.
2
9) Complete the table :
Shape No. of
Faces
No. of
Vertices
No. of
Edges
Triangular Prism 6
Cube 12
2
10) Give expressions of the following:
(a) 8 added to twice a number
(b) 1 less than the product of 12 and p
2
11) Solve and show the following on the number line : 5 + ( - 7)
2
12) Write : (a) 1.77 as a fraction
(b) 12
5 as a decimal.
2
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SECTION C
(Question numbers 13 to 22 carry three marks each)
13) A floor is 5m long and 4m wide. A square carpet of side 3m is laid on the floor,
find the area of the floor that is not carpeted.
3
14) Draw a line AB. Take a point P outside it. Draw a line passing through P and
perpendicular to AB.
3
15) Divide 25 pens between Sheela and Ram in the raio of 3 : 2
3
16) Construct with ruler and compasses, an angle of measure 120° and write the
steps of construction.
3
17) Find the cost of fencing a rectangular field 80 m long and 35 m wide at the rate
of Rs 15 per meter.
3
18) Puneeta is ‘y’ years old. Presently her father is 3 times her age and her mother
is 5 years younger than her father. Write an algebraic expression for the
following:
(a) Puneeta’s age 5 years ago.
(b) Her father’s present age.
(c) Her mother’s present age.
3
19) Rahul bought 4 kg 90 g of apples, 2 kg 60 g of grapes and 5 kg 300 g of
mangoes. Find the total weight of all the fruits he bought.
3
20) (a) Name the geometrical instrument used to measure angles.
(b) Name the unit used to measure angles.
(c) What instruments should be used to compare line segments in the best
possible way.
3
21) Name the following :
(a) The angle name for one-fourth revolution.
(b) The triangle with all three sides of different lengths.
(c) Direction you will face if you start facing east and make half of a revolution
clockwise.
3
22) Fill in the blanks:
(a) 4.15 ______ 4.5 (Put <, > or =)
(b) Rs 5 and 5 paise = Rs _______(write as a decimal)
3
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(c) 300 + 5 + 7
100 = _________ (write as a decimal)
SECTION D
(Question numbers 23 to 30 carry four marks each)
23) Solve :
(a) + 3 + (- 9) + (+2)
(b) (- 4) – (- 11)
4
24) Determine whether the ratios 10 : 18 and 15 : 27 are in proportion (Show the
relevant steps). Also, write the middle terms and the extreme terms, if they are
in proportion.
4
25) Construct PQ =10.3 cm. divide it into four equal parts.
4
26) Draw an angle of 90° and construct its bisector, with the help of compasses and
ruler.
4
27) The cost of 15 stamps is Rs 180.
(a) What will be the cost of 24 such stamps?
(b) How many stamps can be bought in Rs 216?
4
28) (a) Find the area of the following figure (the side of each small square is 1 cm):
(b) How many tiles whose length and breadth are 12 cm and 5 cm respectively
will be needed to fit in a rectangular region whose length and breadth are
100 cm and 144 cm respectively?
1
3
29) (a) Name the type of the following triangles :
(i) ∆ DEF with ∠E = 90° and DE = EF
(ii) ∆ABC with AB = 7.8 cm, AC = 7 cm and BC = 8 cm
(b) Name the type of quadrilateral which :
(i) has all its sides equal but all angles need not be equal
(ii) has only one pair of opposite sides parallel.
2
2
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30) What is the scale of this bar graph? Choose the correct answer from the four
given options.
(a) I unit = 1 year
(b) I unit = 1 student
(c) I unit = 10 students
(d) 1 student = 1 year
Following is the pictograph of the number of wrist watches manufactured by a
factory in a particular week.
(a) On which day were the least number of wrist watches manufactured?
(b) On which day was the maximum number of wrist watches
manufactured?
(c) Find out the approximate number of wrist watches manufactured in
the particular week?
2
2
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